6.10 : Space Trusses

A space truss is a three-dimensional counterpart of a planar truss. These structures consist of members connected at their ends, often utilizing ball-and-socket joints to create a stable and versatile framework. The space truss is widely used in various construction projects due to its adaptability and capacity to withstand complex loads.

At the core of a space truss lies the fundamental unit known as the tetrahedron. This structure is composed of six members that form a three-dimensional shape with four triangular faces. By strategically adding a joint and three additional members to the basic tetrahedral element, a network of interlinked tetrahedrons can be created. This process allows for the construction of increasingly complex space trusses, which can be tailored to meet the demands of various architectural and engineering projects.

For accurate analysis, the space truss members are considered two-force members only if specific conditions are met. These conditions include the application of external loading exclusively at the idealized ball-and-socket joints and the members' weight being negligible. In cases where welded or bolted connections are used, the members must intersect at a common point to satisfy the two-force member condition. When the weight of a member is significant, half of its magnitude is applied as equally distributed vertical forces at both ends of the member.

Equilibrium equations ensure the stability and integrity of a space truss. These equations guarantee that the forces and moments acting on the truss are balanced, preventing any unwanted deformation or failure of the structure. The rigidity and determinacy of a space truss are essential factors in its structural performance. These characteristics necessitate that the number of members (m) and the number of joints (n) within the truss are related through a specific equation.